what`s the difference bt (( backing , backup )) ?????
1 - The police had backup from the army.
2 -We need to get the backing of someone in authority.

Question

what`s the difference bt (( backing  ,  backup )) ?????
1 - The police had backup from the army. 
 2 -We need to get the backing of someone in authority.

Answer

Good question! Both mean to help or support but as you've identified they are not entirely interchangeable. When you are talking about physical support you use backup, not backing. In your second example backing implies authorization. Backup does not have this alternative meaning.